"Discrimination should have no place in a new country," Catherine Ashton told an audience of mainly women in the Libyan capital.
Ashton was speaking during a whirlwind visit to Tripoli, where she inaugurated the EU's mission, which is intended to help coordinate aid efforts for Libya.
The EU struggled during the early days of the Libyan revolution to find a common policy. France, Britain and then NATO carried out a military operation to protect civilians -- an operation thought to be crucial to the success of the campaign by Libyan rebels.
But the EU has since been active in working for the reconstruction of the country. It has been the biggest contributor of humanitarian assistance there, donating 155 million euros ($213 mln) so far, according to EU diplomats.
Ashton toured the capital's Martyrs' Square, where she picked up a bracelet, t-shirt and pendant commemorating the liberation of Libya from deposed leader Muammar Gaddafi.
She was scheduled later in the day to meet Mustafa Abdel Jalil, head of the ruling National Transitional Council, and the country's incoming prime minister, Abdurrahim El-Keib, becoming the first western leader to meet Keib since he took office.
"This is your country," she told diplomats and Libyan representatives at the EU's new mission. "We are here to help and support."
She told an audience of women to "make sure that your new constitution enshrines women's rights."
"You need to find ways to turn laws into practical reality," she added. ($1 = 0.728 Euros) (Reporting by Sebastian Moffett; Editing by Francois Murphy and Sophie Hares)